Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory
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DOI：
10.1115/1.1410100
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发表时间：
2001-12
影响因子：
3.3
通讯作者：
A. Shabana;R. Y. Yakoub
中科院分区：
文献类型：
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作者：
A. Shabana;R. Y. Yakoub
仅用中心线位移来描述梁单元，会给扭转和剪切效应的表达带来困难。例如，这样的表示不捕获梁作为刚体围绕其自身轴的旋转。在文献中，通过在增量有限元法中使用局部坐标系或通过使用多体浮动参考系来规避这个问题。使用这种局部单元坐标系导致作为大单元旋转的结果的惯性力的高度非线性表达式。本文提出了一种用于三维梁单元大转动和大变形分析的绝对节点坐标列式。这个公式导致一个恒定的质量矩阵，因此，离心力和科里奥利力的矢量都等于零。本文提出的公式考虑了转动惯量、扭转和剪切的影响，并保证了斜率的连续性和梁截面在节点处的转动。使用所提出的公式可以系统地模拟曲梁。
The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.